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Simplifying 10x4 + -6x2 + -14 = 0 Reorder the terms: -14 + -6x2 + 10x4 = 0 Solving -14 + -6x2 + 10x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -3x2 + 5x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -3x2 + 5x4)' equal to zero and attempt to solve: Simplifying -7 + -3x2 + 5x4 = 0 Solving -7 + -3x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -0.6x2 + x4 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.6x2 + 1.4 + x4 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.6x2 + x4 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.6x2 + x4 = 0 + 1.4 -0.6x2 + x4 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.6x2 + x4 = 1.4 The x term is -0.6x2. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x2 + 0.09 + x4 = 1.4 + 0.09 Reorder the terms: 0.09 + -0.6x2 + x4 = 1.4 + 0.09 Combine like terms: 1.4 + 0.09 = 1.49 0.09 + -0.6x2 + x4 = 1.49 Factor a perfect square on the left side: (x2 + -0.3)(x2 + -0.3) = 1.49 Calculate the square root of the right side: 1.220655562 Break this problem into two subproblems by setting (x2 + -0.3) equal to 1.220655562 and -1.220655562.Subproblem 1
x2 + -0.3 = 1.220655562 Simplifying x2 + -0.3 = 1.220655562 Reorder the terms: -0.3 + x2 = 1.220655562 Solving -0.3 + x2 = 1.220655562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x2 = 1.220655562 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x2 = 1.220655562 + 0.3 x2 = 1.220655562 + 0.3 Combine like terms: 1.220655562 + 0.3 = 1.520655562 x2 = 1.520655562 Simplifying x2 = 1.520655562 Take the square root of each side: x = {-1.233148637, 1.233148637}Subproblem 2
x2 + -0.3 = -1.220655562 Simplifying x2 + -0.3 = -1.220655562 Reorder the terms: -0.3 + x2 = -1.220655562 Solving -0.3 + x2 = -1.220655562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x2 = -1.220655562 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x2 = -1.220655562 + 0.3 x2 = -1.220655562 + 0.3 Combine like terms: -1.220655562 + 0.3 = -0.920655562 x2 = -0.920655562 Simplifying x2 = -0.920655562 Reorder the terms: 0.920655562 + x2 = -0.920655562 + 0.920655562 Combine like terms: -0.920655562 + 0.920655562 = 0.000000000 0.920655562 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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